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For the system x + a y = 0, y + a z = 0, z + a x = 0, find the set of all real values of a for which the system has a unique solution.

1. {1, -1}
2. R - {-1}
3. {1, 0, -1}
4. R - {1}

Correct answer: R - {-1}

Solution

The determinant is a³ + 1, which is zero only for the real value a = -1, so the unique solution exists for all real a except -1.

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